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In this paper, an adaptive neural terminal sliding mode is implemented for tracking control of magnetic levitation systems with the presence of dynamical uncertainty and exterior perturbation. By proposing a novel fast terminal sliding manifold function with the dynamic coefficients, the system state variables quickly converge the equilibrium point on the manifold function. Besides, an adaptive, robust reaching control law combined with radial basis function neural network compensator drives the system fast approaching the sliding manifold function regardless of whether the initial value is near or far from the sliding manifold and reduces the chattering of the conventional terminal sliding mode control. With a design approach based on the combination of the proposed sliding manifold and the combined control law, the implemented control method provides a control performance with significant improvement in the terms of chattering reduction, high tracking accuracy, fast convergence along with simple design for real applications. The experimental work is implemented for a real magnetic levitation system to demonstrate the superior efficiency of the proposed terminal sliding mode control. The stable evidence of the proposed method is also completely verified by Lyapunov-based method.

Many terminal sliding mode controllers (TSMCs) have been suggested to obtain exact tracking control of robotic manipulators in finite time. The ordinary method is based on TSMCs that secure trajectory tracking under the assumptions such as the known robot dynamic model and the determined upper boundary of uncertain components. Despite tracking errors that tend to zero in finite time, the weakness of TSMCs is chattering, slow convergence speed, and the need for the exact robot dynamic model. Few studies are handling the weakness of TSMCs by using the combination between TSMCs and finite-time observers. In this paper, we present a novel finite-time fault tolerance control (FTC) method for robotic manipulators. A finite-time fault detection observer (FTFDO) is proposed to estimate all uncertainties, external disturbances, and faults accurately and on time. From the estimated information of FTFDO, a novel finite-time FTC method is developed based on a new finite-time terminal sliding surface and a new finite-time reaching control law. Thanks to this approach, the proposed FTC method provides a fast convergence speed for both observation error and control error in finite time. The operation of the robot system is guaranteed with expected performance even in case of faults, including high tracking accuracy, small chattering behavior in control input signals, and fast transient response with the variation of disturbances, uncertainties, or faults. The stability and finite-time convergence of the proposed control system are verified that they are strictly guaranteed by Lyapunov theory and finite-time control theory. The simulation performance for a FARA robotic manipulator proves the proposed control theory’s correctness and effectiveness.

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